南方科技大学知识苑(SUSTech KC): On the Quantum K-Theory of the Quintic

题名	On the Quantum K-Theory of the Quintic
作者	Garoufalidis, Stavros1 ; Scheidegger, Emanuel 2
通讯作者	Garoufalidis, Stavros
发表日期	2022
DOI	10.3842/SIGMA.2022.021
发表期刊	Symmetry Integrability and Geometry-Methods and Applications 影响因子和分区
ISSN	1815-0659
卷号	18
摘要	Quantum K-theory of a smooth projective variety at genus zero is a collection of integers that can be assembled into a generating series J(Q, q, t) that satisfies a system of linear differential equations with respect to t and q-difference equations with respect to Q. With some mild assumptions on the variety, it is known that the full theory can be reconstructed from its small J-function J(Q, q, 0) which, in the case of Fano manifolds, is a vector-valued q-hypergeometric function. On the other hand, for the quintic 3-fold we formulate an explicit conjecture for the small J-function and its small linear q-difference equation expressed linearly in terms of the Gopakumar-Vafa invariants. Unlike the case of quantum knot invariants, and the case of Fano manifolds, the coefficients of the small linear q-difference equations are not Laurent polynomials, but rather analytic functions in two variables determined linearly by the Gopakumar-Vafa invariants of the quintic. Our conjecture for the small J-function agrees with a proposal of Jockers-Mayr.
关键词	quantum K-theory quantum cohomology quintic Calabi-Yau manifolds Gromov-Witten invariants Gopakumar-Vafa invariants q-difference equations q-Frobenius method J-function reconstruction gauged linear sigma models 3d-3d correspondence Chern- Simons theory q-holonomic functions
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	第一 ; 通讯
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000773400000001
出版者	NATL ACAD SCI UKRAINE, INST MATH
来源库	Web of Science
引用统计	被引频次[WOS]：3
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/328456
专题	理学院_数学系深圳国际数学中心（杰曼诺夫数学中心）（筹）
作者单位	1.Southern Univ Sci & Technol, Int Ctr Math, Dept Math, Shenzhen, Peoples R China 2.Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China
第一作者单位	数学系
通讯作者单位	数学系
第一作者的第一单位	数学系
推荐引用方式 GB/T 7714	Garoufalidis, Stavros,Scheidegger, Emanuel. On the Quantum K-Theory of the Quintic[J]. Symmetry Integrability and Geometry-Methods and Applications,2022,18.
APA	Garoufalidis, Stavros,&Scheidegger, Emanuel.(2022).On the Quantum K-Theory of the Quintic.Symmetry Integrability and Geometry-Methods and Applications,18.
MLA	Garoufalidis, Stavros,et al."On the Quantum K-Theory of the Quintic".Symmetry Integrability and Geometry-Methods and Applications 18(2022).